# std::sph_bessel, std::sph_besself, std::sph_bessell

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< cpp‎ | numeric‎ | special functions

Defined in header `<cmath>` |  |
| (1) |
float sph_bessel ( unsigned int n, float x ); double sph_bessel ( unsigned int n, double x ); long double sph_bessel ( unsigned int n, long double x ); |  | (since C++17) (until C++23)
/*floating-point-type*/ sph_bessel( unsigned int n, /*floating-point-type*/ x ); |  | (since C++23)
float sph_besself( unsigned int n, float x ); | (2) | (since C++17)
long double sph_bessell( unsigned int n, long double x ); | (3) | (since C++17)
Additional overloads |  |
Defined in header `<cmath>` |  |
template< class Integer > double sph_bessel ( unsigned int n, Integer x ); | (A) | (since C++17)

1-3) Computes the spherical Bessel function of the first kind of n and x. The library provides overloads of `std::sph_bessel` for all cv-unqualified floating-point types as the type of the parameter x.(since C++23)
A) Additional overloads are provided for all integer types, which are treated as double.

### Parameters

n | - | the order of the function
x | - | the argument of the function

### Return value

If no errors occur, returns the value of the spherical Bessel function of the first kind of n and x, that is jn(x) = (π/2x)1/2
Jn+1/2(x) where Jn(x) is std::cyl_bessel_j(n, x) and x≥0.

### Error handling

Errors may be reported as specified in math_errhandling.

- If the argument is NaN, NaN is returned and domain error is not reported.
- If n≥128, the behavior is implementation-defined.

### Notes

Implementations that do not support C++17, but support ISO 29124:2010, provide this function if `__STDCPP_MATH_SPEC_FUNCS__` is defined by the implementation to a value at least 201003L and if the user defines `__STDCPP_WANT_MATH_SPEC_FUNCS__` before including any standard library headers.

Implementations that do not support ISO 29124:2010 but support TR 19768:2007 (TR1), provide this function in the header `tr1/cmath` and namespace `std::tr1`.

An implementation of this function is also available in boost.math.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::sph_bessel(int_num, num) has the same effect as std::sph_bessel(int_num, static_cast<double>(num)).

### Example

Run this code

    #include <cmath>
    #include <iostream>

    int main()
    {
        // spot check for n == 1
        double x = 1.2345;
        std::cout << "j_1(" << x << ") = " << std::sph_bessel(1, x) << '\n';

        // exact solution for j_1
        std::cout << "sin(x)/x² - cos(x)/x = "
                  << std::sin(x) / (x * x) - std::cos(x) / x << '\n';
    }

Output:

    j_1(1.2345) = 0.352106
    sin(x)/x² - cos(x)/x = 0.352106

### See also

cyl_bessel_jcyl_bessel_jfcyl_bessel_jl (C++17)(C++17)(C++17) | cylindrical Bessel functions (of the first kind) (function)
sph_neumannsph_neumannfsph_neumannl (C++17)(C++17)(C++17) | spherical Neumann functions (function)

### External links

Weisstein, Eric W. "Spherical Bessel Function of the First Kind." From MathWorld — A Wolfram Web Resource.

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